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Integrating Using Arctan

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data
    1/(x2 +11x +29)

    2. Relevant equations

    3. The attempt at a solution
    I'm doing something wrong, but can't figure out what...

    Complete the square so that the denominator equals (x+2)2+25

    Then divide by 25: ((x+2)2)/25 + 1

    Move that 25 into the squared part: ((x+2)/5)2+1

    Substitute the squared part for u.

    Find du/dx = 1/5, and therefore 5du=dx

    Now we have 5*(integral sign) du / (u2+1)

    This gives 5arctan(u)+C --> substitute u back for what you had before.

    But the answer is 1/5arctan(u). Where did I go wrong?
    Last edited: Feb 1, 2009
  2. jcsd
  3. Feb 1, 2009 #2
    When you "divide by 25", where does that 25 go?
  4. Feb 1, 2009 #3
    Oops, I was focusing so much on the denominator, I forgot about the numerator. This is what happens when yiou do math late at night, haha.

  5. Feb 1, 2009 #4


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    Science Advisor
    Homework Helper

    You can't just divide by something and expect the answer to be unchanged. Once you have 1/((x+5)^2+25) why not just substitute (x+5)=5*u?
  6. Feb 2, 2009 #5


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    Gold Member

    how about x+2 = 5tanu to make life easier
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